Lady Gaga's Fan Sing-Along Silences the Crowd at Chateau Marmont

West Hollywood's Chateau Marmont is a bustling venue, but when Lady Gaga arrived for drinks on Tuesday night, the entire restaurant fell silent.

"While walking back from the bathroom, Gaga stopped in her tracks when she heard a small group of people singing her song 'Edge of Glory,' " an onlooker tells PEOPLE. "The singing was very loud and made all the guests stop their conversation."

Looking into it further, Gaga and her three male companions, who looked like bodyguards, realized the voices were coming from a large group of fans camped out on the other side of the hotspot's wall of hedges.

"Gaga tried to speak to the fans through the wall but the singing was too loud so she had the hedges pulled apart as she stuck her head through the wall," the source says. "She said, 'Guys, it's Gaga,' before the crowd exploded with cheers."

Chatting with the fans for a few minutes while sticking her head through the bush, the insider explains, "Gaga told them she loved them and appreciated the support, but to please stop singing so the other people inside could eat in peace."

As the fans apparently happily obliged, Gaga – dressed in "an amazingly insane black outfit" – joined a girlfriend at the bar to chat while sipping on a glass of wine.